Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
2'95085
TRANSMISSION LINE POWER CONTROLLER WITH A CONTINUOUSLY
CONTROLLABLE VOLTAGE SOURCE RESPONSIVE TO A REAL POWER
DEMAND AND A REACTIVE POWER DEMAND
Brief Description of the Invention
This invention relates generally to the control of bulk
electrical power on a transmission line. More particularly,
this invention relates to a unified power flow control
apparatus with a continuously controllable voltage source that
produces a desired real and reactive power flow on a three-
phase transmission line.
Background of the Invention
A generalized power flow controller is described by
Gyugyi, et al, in U.S. Patent Number 5,343,139, entitled
"Generalized Fast, Power Flow Controller" (the Gyugyi patent).
This device is referred to as a Unified Power Flow Controller
(UPFC). The architecture of a UPFC implementation is
illustrated in Figure 1.
This implementation of the UPFC 20 includes a parallel
inverter 22 connected to a series inverter 24 through a do link
26. The inverters of Figure 1 each include six semiconductor
switches 28, such as Gate-Turn-Off (GTO) thyristors, each of
which is shunted by a reverse-parallel connected diode 30. The
UPFC 20 is connected to a transmission line 34 through a shunt
transformer 36 and a series transformer 38. As used herein,
the term transmission line includes the three lines of a three-
phase transmission system.
A
PCT/US95/07600
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In accordance with the prior art, the UPFC 20
includes a controller 40 that executes a control
strategy based upon the emulation of conventional power
line control devices, such as thyristor-controlled
series capacitors or thyristor-controlled phase angle
regulators. That is, the controller 40 monitors
selected line parameters and in response thereto, fires
the switches 28 to realize a conventional power line
control strategy.
In general, the UPFC 20 functions as an ac to ac
power converter in which real power can freely flow in
either direction between the ac terminals of the two
inverters. In addition, each inverter can independently
generate or absorb reactive power at its own ac output
terminal.
The series inverter 24 can be regarded as a series
voltage source with controllable magnitude and angle.
The parallel inverter 22 can be regarded as a unity
power factor current source with a magnitude that is
sufficient to ensure that the real power drawn by the
shunt device is equal and opposite to the real power
drawn by the series device.
The series inverter 24 provides the main function
of the UPFC 24 by injecting, through series transformer
38, an ac voltage Vpq with controllable magnitude and
phase angle with respect to the phase of the
transmission line voltage. This injected series voltage
can be considered as a synchronous ac voltage source.
In the prior art, selection of magnitude and phase angle
of the injected voltage Vpq has been used to adjust any
one or more of the following system parameters:
transmission line voltage magnitude, transmission line
impedance, and transmission line voltage phase angle.
The real power that is injected by the series
inverter 24 is obtained from the parallel inverter 22.
The parallel inverter 22 supplies or absorbs real power
through the shunt transformer 36. The parallel inverter
22 can also generate or absorb controllable reactive
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power at the shunt transformer 36, and thereby it can
provide independent shunt reactive compensation for the
line.
The flow of real power in or out of the do link 26
is determined by the phase angle of the ac voltage
generated by the parallel inverter with respect to the
ac system voltage. The flow of reactive power to or
from the parallel inverter is determined by the
amplitude difference between the ac voltage signal of
the parallel inverter 22 and the ac voltage signal on
transmission line 34. If the amplitude of the ac
voltage signal from the parallel inverter 32 is larger
than the amplitude of the ac voltage signal on
transmission line 34, then the parallel inverter 22
supplies capacitive reactive power. If the amplitude of
the ac voltage signal from the parallel inverter 32 is
smaller than the amplitude of the ac voltage signal on
transmission line 34, then the parallel inverter 22
consumes inductive reactive power.
It should be noted that there is a closed path for
real power from the transmission line 34, through the
shunt transformer 36, through the parallel inverter 22,
through the do link 26, through the series inverter 24,
and through the series transformer 38 back to the
transmission line 34. In contrast, the corresponding
reactive power is supplied or absorbed locally by the
parallel inverter 22 and therefore it does not flow
through the line. Thus, the parallel inverter 22 can be
operated at a unity power factor or it can be controlled
to have a reactive power exchange with the line
independently of the reactive power exchanged by the
series inverter. Consequently, there is no continuous
reactive power flow through the UPFC 20.
The basic operations of the parallel inverter and
the series inverter may be established by any number of
well known techniques, such as pulse-width modulation
(PWM). Regardless of the technique selected, the
parallel inverter maintains the do link voltage at an
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essentially constant level that corresponds to the
highest output voltage produced by either inverter.
As previously indicated, UPFCs 20 are
conventionally controlled from the standpoint of
existing power transmission practices based on reactive
shunt compensation, series compensation, and phase
shifting. For example, terminal voltage regulation can
be achieved when Vpq is injected in-phase or anti-phase
with the line voltage V to produce conditioned line
l0 voltage V'. To provide series capacitive compensation,
Vpq is injected in quadrature with the line current I.
Transmission angle regulation is achieved when Vpq is
injected with an angular relationship with respect to V
that achieves the desired phase shift (advance or
retard) without any change in magnitude.
The Gyugyi patent mentioned above relies upon these
traditional paradigms to control the UPFC. In
particular, the patent states that the controller is
used to operate the parallel inverter and series
inverter in a coordinated manner to ensure that: "(1)
the ac output voltage of the [series inverter is]
injected in phase to meet the instantaneous requirements
of the controlled system parameters (line impedance,
phase-angle, voltage magnitude) at the output end of the
[series transformer] for optimum power transfer, as
dictated by the relevant reference signals supplied to
the [controller 40], and (2) the ac output voltage of
[the parallel inverter is] coupled to the ac system by
the [shunt transformer and] has the proper magnitude and
phase-angle to provide the real power demand of the
[series inverter] and to generate or absorb the reactive
power at the input end of the [series transformer] to
regulate the voltage at that point according to an
externally defined reference." The patent later
indicates that the externally defined reference signals
are the only control inputs to the system. One
reference signal is a voltage magnitude signal to the
shunt inverter control (T*) and the other reference
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signal is an angle reference signal (a*). Thus, the
prior art is concerned with directing the switching
activity within the power electronic circuits of the
UPFC 20 such that the UPFC 20 operates as conventional
power line control devices.
One shortcoming of the approach of controlling a
UPFC 20 to emulate conventional power line control
devices is that previously these devices have been used
individually. Consequently, no rules exist for using
them together to achieve an optimal control of power
flow.
It would be desirable to introduce a completely new
paradigm for the control of power transmission lines.
That is, it would be desirable to develop a new
transmission line power control system that does not
rely upon the emulation of conventional power line
control devices.
Summary of the Invention
The invention is a transmission line power
controller for controlling the flow of electric power in
an alternating current three-phase transmission system.
The preferred implementation of the power line
controller includes a parallel inverter connected to a
series inverter through a do link. The parallel
inverter is connected in shunt to the transmission
system through a shunt transformer. The series inverter
is connected in series with the transmission system
through a series transformer. A transmission line
power control circuit is used to specify a desired real
power demand and reactive power demand for the
transmission system. The power control circuit
processes this information along with a transmission
line voltage vector and a transmission line current
vector to produce a voltage source reference signal that
is applied to the series inverter. In response to the
voltage source reference signal, the series inverter
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produces an injected voltage vector into the transmission
system. The injected voltage vector farces the transmission
line current vector to a desired value corresponding to the
specified real power and reactive power demand. Thus, desired
real power and reactive power flow is rapidly achieved on the
transmission system.
According to one aspect the invention may be summarized as
a transmission line power controller for controlling the flow
of electric power in an alternating current transmission system
including a three-phase transmission line, comprising:
continuously controllable voltage sources connected in series
with each of the phases of said three-phase transmission line
to provide an injected voltage; power transducers connected to
said three-phase transmission line to produce a current signal
representative of the instantaneous current values of each of
said phases of said three-phase transmission line and to
produce a voltage signal representative of the instantaneous
voltage values of each of said phases of said three-phase
transmission line; a real power flow specification device to
receive a real power flow demand; a reactive power flow
specification device to receive a reactive power flow demand;
and a power control circuit connected to said continuously
controllable voltage sources, said power transducers, said real
power flow specification device, and said reactive power flow
specification device, said power control circuit processing
said current signal, said voltage signal, said real power flow
demand, and said reactive power flow demand to generate a
voltage source reference signal that is applied to said
continuously controllable voltages sources to produce said
injected voltage such that the injected voltage forces the
transmission line current to a desired value corresponding to
said real power demand and said reactive power demand.
According to another aspect the invention may be
summarized as a transmission line power flow controller to
control the flow of electric power on an alternating current
transmission system, comprising: a transmission line power
control circuit to produce a voltage source reference signal
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from a real power flow demand signal, a reactive power flow
demand signal, and sampled power signals from said alternating
current transmission system; and a series inverter connected to
said transmission line power control circuit to process said
voltage source reference signal and generate an injected
voltage which is applied to said alternating current
transmission system to force the current of said alternating
current transmission system to a desired value corresponding to
said real power flow demand signal and said reactive power flow
demand signal.
Brief Description of the Drawings
For a better understanding of the nature and ob~ects of
the invention, reference should be made to the following
detailed description taken in conjunction with the accompanying
drawings, in which:
FIGURE 1 is an illustration of a prior art unified power
f low cont roller .
FIGURE 2 is an illustration of the transmission line power
controller of the present invention.
FIGURE 3 depicts an embodiment of the power controller of
the power control circuit of the invention.
FIGURE 4 illustrates one embodiment of the vector control
loop compensator of the power control circuit of the invention.
FIGURE 5 is a vectorial representation of the vector
control loop compensator of the invention.
FIGURE 6 is an alternate embodiment of the vector control
loop compensator to be used to eliminate power oscillations or
rapid power transients.
FIGURE 7 is an alternate embodiment of the synchronous
reference frame processor of the vector control loop
compensator.
FIGURE 8 is an alternate embodiment of the vector control
loop compensator to be used to eliminate a negative sequence
1 ine component .
Like reference numerals refer to corresponding parts
throughout the several views of the drawings.
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Detailed Description of the Invention
Figure 2 illustrates a transmission line power
controller 50 in accordance with the invention. The
transmission line power controller 50 includes a number
of elements previously described in relation to the
prior art unified power flow controller. In particular,
the figure illustrates a parallel inverter 22 connected
to a series inverter 24 through a do link 26. The
parallel inverter 22 is connected in shunt to a three-
phase transmission line 34 through a shunt transformer
36. The series inverter 24 is connected to the three-
phase transmission line 34 through a series transformer
38.
In accordance with the invention, control of the
parallel inverter 22, series inverter 24, and do link 26
is accomplished through the transmission line power
control circuit 52 of the invention. The transmission
line power control circuit 52 includes a power
controller 54 and a vector control loop compensator 56.
A set of conventional power transducers 58 are used
in a feedback control loop to continuously generate a
transmission line current vector signal I~ and a
transmission line voltage vector signal V~. The power
controller 54 receives the transmission line voltage
vector signal V~, a real power demand (P), and a
reactive power demand (Q). The real power demand may be
established through a real power flow specification
device. This device may be a supervisory computer
system, a keyboard, an analog dial, a thumb-wheel
switch, etc. A reactive power flow specification device
is similarly used to obtain the reactive power demand.
These signals are processed by the power controller
54 to produce a current control reference signal I~ref~
which is processed by the vector control loop
compensator 56 to produce a voltage source reference
signal V~S ref' The voltage source reference signal V~S ref
is processed by the series inverter 24 in a conventional
manner to generate an injected voltage vector V~~n~. The
9~~ ~~
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injected voltage vector V~~n~ forces the transmission line
current vector I" to a desired value corresponding to
the real power demand P and the reactive power demand Q.
Thus, at the point of sampling at the power transducers
58, the power on the transmission line corresponds to
the real power demand P and the reactive power demand Q.
In sum, the transmission line power controller 50
of the invention uses the injected voltage vector V~ln~ as
a controllable vector forcing function to force the
transmission line current vector I~ to produce desired
real power and reactive power flow on the transmission
line. The injected voltage vector is established by the
power control circuit 52 as it monitors the transmission
line voltage V~ and continuously calculates the
appropriate current reference for a desired real power
(P) and reactive power (Q).
The automatic control of an injected series voltage
vector to maintain a demanded P,Q condition on a
transmission line is believed to be a new concept. Note
that the power control circuit 52 is not intended to
simply reproduce the actions of conventional equipment
such as, mechanical or thyristor-controlled phase angle
regulators, load tap-changes, and series capacitors.
That is, the power control circuit 52 does not rely upon
a strategy of changing the line parameters to accomplish
an intended result. Instead, the power control circuit
52 uses closed-loop feedback control along with P and Q
demands to continuously calculate the necessary injected
voltage vector. That is, the power control circuit 52
controls the magnitude and angular position of the
injected voltage vector in real time so as to maintain
or vary the real and reactive power flow on the line to
satisfy load demand and system operating conditions.
The power control circuit 52 uses established
techniques to control the parallel inverter 22. In this
regard, the power control circuit 52 acts to maintain a
preset voltage level on the do link 26, thereby ensuring
the required real power balance between the parallel
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inverter 22 and the series inverter 24. Since this
operation is known in the art, attention turns to a more
detailed consideration of the operation of the power
control circuit 52 to produce the voltage reference
signal that is used by the series inverter 24 to
generate the injected voltage vector.
Figure 3 is a detailed representation of one
embodiment of the power controller 54 of the power
control circuit 52. In this embodiment, a 3-to-2 phase
transformer 70 is used to transform the three-phase
voltage vector V~ (Va, Vb, Vc) into a two-phase d-q
quantity that is stationary with respect to the three-
phase system. The 3-to-2 phase transformer 70 relies
upon synchronous control. Real-time control using
synchronous control concepts is known in ac motor
control and active power line conditioning. U.S. Patent
5,287,288 (the '288 patent), assigned to the assignee of
the present invention, and expressly incorporated by
reference herein, discloses the use of synchronous
control in active power line conditioning.
While synchronous control has been used in active
power line conditioners (APLC), it is important to note
the distinctions between the active power line
conditioning technical field and the technical field of
the present invention. The present invention is
directed toward a power transmission line transmitting
power from one voltage-regulated bus to another. An
APLC provides power conditioning between a distribution
feeder and one or more loads. In other words, an APLC
provides a buffering action between a power supply and a
load. More particularly, an APLC is concerned with
providing sinusoidal voltages to the load and passing
sinusoidal currents back to the supply. An'APLC does
not in any sense attempt to determine the real power
flow between the supply and the load. It is ~e load
that determines the power flow, and the APLC attempts
primarily to remove harmonic content from the load
voltage and the supply current. In contrast, the
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present invention teaches how to regulate the power flow
between two voltage buses to a desired value, and is not
concerned with harmonic content. Thus, the present
invention uses different processing techniques and
generates different reference signals.
In any event, the '288 patent and other references
fully describe synchronous control. However, for the
sake of completeness, it will be appreciated that the 3-
to-2 phase transformer 76 executes the following
l0 equation:
V 1 -1/2 -1/2 Va
2 3 0 -~/2 ~/2~ V
r
The derived d-q line voltage signals Vd and Vq are
then processed by the voltage magnitude and phase angle
processor 72. The voltage magnitude and phase angle
processor 72 derives a transmission line phase angle
signal B and a transmission line voltage magnitude
signal V~mag. These quantities may be obtained with the
following equations:
B = arctan(Vd/Vq) (Equation 1)
V~mag = ((Vd)2 + (Vq)2)l~ (Equation 2)
Other techniques may be used to derive these quantities.
For example, the '288 patent discloses the use of a
phase-locked loop to obtain the value B.
Figure 3 also illustrates a power demand processor
76 that is used to generate a complex power demand
signal S and a power factor demand ~. These quantities
are calculated based upon the previously described real
power demand P and reactive power demand Q. To obtain
the. complex power demand signal and the power factor
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demand signal, the following equations may be executed
by the power demand processor 76
S = (P2 + Q2)'~ (Equation 3)
ø~ = arctan (Q/P) (Equation 4).
Figure 3 illustrates that the complex power demand
signal S is divided by the transmission line voltage
magnitude signal at divider 78 to obtain an intermediate
current control reference signal I"iref~ Depending upon
the 3-to-2 phase transformer equations used, the voltage
magnitude signal may have to be multiplied at multiplier
79 by a scaling constant to extract the current signal
from the voltage magnitude signal.
Figure 3 also illustrates that the transmission
line phase angle signal is added to the power factor
demand signal to obtain a current vector reference angle
signal ~. The current vector reference angle signal
and the intermediate current control reference signal
I~~ref are then processed by the D-Q transformer 82. The
D-Q transformer 82 transforms the power coordinates to
rectangular coordinates projected onto the d-q axes.
These values are denominated the d-q current control
reference signals Id ref and Ic~ref~ Note that these
signals constitute the previously described current
control reference signal I~ref. The d-q current control
reference signals Id ref and I~ref may be obtained by using
the following equations:
Id ref - I~ref cos (~) (Equation 5)
IcLref - IAref sin() (Equation 6)
The processing of the power controller 54 to
generate the current control reference signal I~ref has
now been fully described. Attention presently turns to
Figure 4, which is a detailed depiction of one
embodiment of the vector control loop compensator 56 of
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the invention. The vector control loop compensator 56
includes a 3-to-2 phase transformer 70 of the type
previously described. However, note that in this
instance, the 3-to-2 phase transformer 70 operates upon
the transmission line current vector I~, which includes
three-phase components Ia, Ib, Ic. The d-q transmission
line current signals Id and Iq generated by the 3-to-2
phase transformer 70 are subtracted from the previously
described d-q current control reference signals Idref and
I~ref to generate d-q current control error signals Id err
and I~err
Another known synchronous control element, a
stationary-to-rotating processor 90, is used to process
the d-q current control error signals Id err and I~err
This operation may be performed as follows:
(Iq-9-ezzl =f cosh -sin6l Iq-ezr
lId-s-ezzJ lSlue COSe J Id-err
The 8 term was previously obtained by the voltage
magnitude and phase angle processor 72. The output of
the stationary-to-rotating processor 90 is a set of
synchronous d-q current control error signals Id-s-err
.and Iq-s err. These signals are do quantities in the
synchronous reference frame. They correspond to the
fundamental component of the error signal.
The synchronous d-q current control error signals
may now be processed by a synchronous reference frame
processor 92. For the sake of simplicity, only a single
line is shown entering and exiting the synchronous
reference frame processor 92.
In the embodiment of Figure 3, the synchronous
reference frame processor includes an integrator 94 and
a proportional gain element 96. The integrator 94
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serves to provide high gain for the error vector
components. The proportional gain element 96 serves to
stabilize the signal. The outputs of the integrator 94
and proportional gain element 96 result in processed
synchronous d-q current control error signals Id ps err
and Iq_ps err.
A rotating-to-stationary processor 100 is then used
to remove the signals from the synchronous reference
frame. The following equations may be used for this
operation:
(Iq-p-errl =~ COSe SiIlel Iq-ps-erz
ILLld-p-errJJI -S1I18 COSeJ Id-ps-err
This operation produces stationary reference frame
processed d-q current control error signals Id_p err and
Iq p err. These signals are then transformed to a
three-phase signal with a 2-to-3 phase transformer 102
that executes the following equation:
Va-ref 1 0
Vb-ref = 3 -1/2 -~/2 f Iq P errJ
Vc-ref ~~ LId-P-err
l-1/2 ~/2
The 2-to-3 phase transformer 102 yields three-phase
reference signals Va ref, Vb ref, and Vc ref. Note that
these signals are equivalent to the previously described
voltage source reference signal V"Sref~ As previously
indicated, the voltage source reference signal V"Sref is
then applied to the series inverter 24 by means of an
appropriate modulator (such as a PWM) as known by those
skilled in the art. This operation forces the series
inverter 24 to generate the previously described
injected voltage vector V"ink, which forces the line
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current vector I~ to a desired value corresponding to
the real and reactive power demand received by the power
control circuit 52.
The operation of one embodiment of the power
control circuit 52 of the invention has now been
described. Attention will now turn to alternate
embodiments of the invention.
Figure 5 illustrates the vector control loop
compensator 56 in vector notation. As in the embodiment
of Figure 4, a 3-to-2 phase transformer 70 is used to
generate two-phase d-q quantities. The signal Iq is
multiplied by a complex component j. Similarly, the q
component (Iq ref -- shown in Figure 3) of the current
control reference signal is multiplied by a complex
component j to yield the current control reference
signal I~ref shown in Figure 5. These signals are
combined to produce a current control error signal I~err
which is applied to a negative vector rotator 110. The
negative vector rotator 110 rotates the error vector
signal I~err negatively through the angle B, derived
from the voltage magnitude and phase angle processor 72.
This produces a synchronous vector error signal that is
processed in the previously described synchronous
reference frame processor 92 to generate a processed
synchronous vector error signal. A positive vector
rotator 112 is then used to positively rotate the
processed synchronous vector error signal through the
angle B. This produces a signal corresponding to the
previously described voltage source reference signal
3 0 V ~ Sref '
Figure 6 illustrates an alternate embodiment of the
vector control loop compensator 56. This embodiment is
similar to the embodiment of Figure 5. However, there
are two major distinctions. First, in this embodiment,
the current control reference signal I~ref is set to
zero. Next, the synchronous reference frame processor
92 includes an additional derivative term S/(1 + sT) in
block 113. This additional term controls the rate of
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change of transmission line power according to the time
constant T. Thus, with the embodiment of Figure 6, the
transient power on the transmission line is controlled
to a desired value of zero. In this configuration, the
power control circuit 52 will not attempt to dictate the
steady state power flow of the line, but will only act
to eliminate power oscillations or rapid power
transients.
Figure 7 illustrates another alternate embodiment
of the synchronous reference frame processor 92. In
this embodiment, the synchronous reference frame
processor 92 only has one term: K(s + jw)/S. This term
has proven to be particularly advantageous as it
provides a more stable response, while compensating for
the line inductance.
Figure 8 is similar to previous embodiments, but
includes an additional rotating frame controller. The
additional controller is synchronous with the vector
representing the negative sequence fundamental frequency
component of the line voltage. That is, the current
control error signal I~err is processed by the negative
vector rotator 110 as previously described, but in
addition, it is processed by a positive vector rotator
112 to process the negative sequence fundamental
frequency component of the line voltage. The negative
sequence fundamental frequency component is processed by
the synchronous reference frame processor 92A and is
then processed by a negative vector rotator 110'. The
output is then combined with the processed positive
sequence fundamental frequency component. The resultant
voltage source reference signal V~sref includes a
negative sequence voltage signal component that will
automatically reduce the negative sequence line current
to zero.
Any of the described embodiments can be used as an
automatic power flow limiter. In this variation, the
power control circuit 52 is kept in an inactive state
(i.e. the series voltage is set to zero) until the
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transmission line power exceeds a preset maximum level.
At this time, the power control circuit 52 is enabled
and is operated in such a way as to limit the power to
the set level. This power limiting embodiment can be
used in any situation where overloading of the line can
produce undesirable effects on power system stability.
Those skilled in the art will recognize a number of
advantages associated with the present invention.
First, the ability to define a real and reactive power
demand opens up a range of possibilities for power
system control. The attainable response of the control
is very fast, almost instantaneous, and thus the
apparatus of the invention is extremely effective in
handling dynamic system disturbances. Apart from the
obvious advantages for power scheduling and automatic
power limiting, the fast dynamic response of the power
controller 50 will automatically prevent power
oscillations from existing on the line and can adapt
almost instantaneously to new real and reactive power
demands to enhance the transient behavior of the system
and optimize its performance under transmission
contingency conditions. In accordance with the
invention, negative sequence line current can be
controlled to zero. This eliminates current unbalance
and restores maximum utilization of the transmission
line. All of these benefits are derived from the
invention's use of a single automatic control system
with a constant loop structure. This technique is
clearly preferable to the many control modes that wold
be required to achieve similar results using existing
passive components.
It will be appreciated by those skilled in the art
that the power control circuit may be implemented in any
number of ways. For instance, the device may hardwired
or implemented as a set of computer programs operating
on a general purpose computer with appropriate
interfaces to the power transducers 58, parallel
inverter 22, and series inverter 24.
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The power controller 50 of the invention has been
described with reference to its preferred embodiment.
However, it should be recognized that the power
controller 50 can also be implemented in other devices
that include at least the series inverter 24. In some
cases these applications involve some restriction in the
operating range compared with the preferred embodiment,
but they are likely to be attractive because of their
lower cost, and relatively high effectiveness in
controlling power flow. These alternative embodiments
all have a series inverter 24 but they differ in regard
to the parallel inverter 22. In particular, the
parallel inverter 22 may be replaced by other devices
that are connected to the do terminals of the series
inverter 24 and are capable of absorbing or supplying
real power on a steady state or transient basis, as
required.
The application of limits on the range of the
series voltage reference signal V"Sref has been omitted
from the figures for clarity. However, it should be
understood that these limits are applied in a physical
embodiment of the invention.
The foregoing descriptions of specific embodiments
of the present invention are presented for purposes of
illustration and description. They are not intended to
be exhaustive or to limit the invention to the precise
forms disclosed, obviously many modifications and
variations are possible in view of the above teachings.
The embodiments were chosen and described in order to
best explain the principles of the invention and its
practical applications, to thereby enable others skilled
in the art to best utilize the invention and various
embodiments with various modifications as are suited to
the particular use contemplated. It is intended that
the scope of the invention be defined by the following
Claims and their equivalents.
